Highest Common Factor of 225, 820, 830 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 225, 820, 830 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 225, 820, 830 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 225, 820, 830 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 225, 820, 830 is 5.
HCF(225, 820, 830) = 5
HCF of 225, 820, 830 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 225, 820, 830 is 5.
Highest Common Factor of 225,820,830 is 5
Step 1: Since 820 > 225, we apply the division lemma to 820 and 225, to get
820 = 225 x 3 + 145
Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 145 and 225, to get
225 = 145 x 1 + 80
Step 3: We consider the new divisor 145 and the new remainder 80, and apply the division lemma to get
145 = 80 x 1 + 65
We consider the new divisor 80 and the new remainder 65,and apply the division lemma to get
80 = 65 x 1 + 15
We consider the new divisor 65 and the new remainder 15,and apply the division lemma to get
65 = 15 x 4 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 225 and 820 is 5
Notice that 5 = HCF(15,5) = HCF(65,15) = HCF(80,65) = HCF(145,80) = HCF(225,145) = HCF(820,225) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 830 > 5, we apply the division lemma to 830 and 5, to get
830 = 5 x 166 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 830 is 5
Notice that 5 = HCF(830,5) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 225, 820, 830 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 225, 820, 830?
Answer: HCF of 225, 820, 830 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 225, 820, 830 using Euclid's Algorithm?
Answer: For arbitrary numbers 225, 820, 830 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
